derivative of-(x-1^2+3)

解

\frac{d}{d x} (- (x - 1)^{2} + 3)

- 2 x + 2

解答ステップ

\frac{d}{d x} (- (x - 1)^{2} + 3)

簡素化

- (x - 1)^{2} + 3 : - x^{2} + 2 x + 2

= \frac{d}{d x} (- x^{2} + 2 x + 2)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d x} (x^{2}) + \frac{d}{d x} (2 x) + \frac{d}{d x} (2)

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (2 x) = 2

\frac{d}{d x} (2) = 0

= - 2 x + 2 + 0

簡素化

= - 2 x + 2